LPQD序列Baum-Katz和Davis大数定律的精确渐近性

Precise asymptotics in the Baum-Katz and Davis law of large numbersfor LQPD sequences

设{X_i,i≥1}是一严平稳零均值LPQD随机变量序列,0<EX_1~2<∞,σ~2=EX_1~2+sum from j=2 to ∞(E(X_1X_j)),并且0<σ~2<∞,令S_n=sum from i=1 to n(X_i),利用部分和S_n的弱收敛定理,证明了当ε→0时,sum from n≥1 to(n^(r/p-2))P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to(1/n)P〔│S_n│≥εn^(1/p)〕,sum from n≥1 to((1n n)~δ/n)P〔│S_n│≥ε(n 1n n)～(1/2)〕的精确渐近性.

Let {Xi,i≥1}be a strictly stationary sequence of LPQD random variables with mean zeros. Let 0〈EX1^2〈∞,σ^2=EX1^2＋∑j=2^∞E（X1Xj）,and 0〈σ^2〈∞,let Sn=∑i=1^nXi,by weak convergence for the partial sum of Sn , the precise asymptotics for ∑n≥1n^r/p-2 P（｜Sn｜≥εn^1/p）,∑n≥11/nP（｜Sn｜≥εn^1/p）,∑n≥1（ln n）^δ/nP（｜Sn｜≥ε√n log n）as ε→0 was established.